Very — Stellar RevoliUio7is within the Galaxy. 133 



is then ten billion kilometers (English numeration). As the 

 distance of the nearest star, a Centaiiri, is forty billion kilo- 

 meters, the adopted radius of the sphere is too small for the 

 assumed nniform distribution ; but for the actual stellar distri- 

 bution it is not an unreasonable value, because of the concen- 

 tration of stars in the galactic centers, and provided the number 

 10^ is acceptable for the total number of stars. Photographs 

 of long exposure with telescopes having a large ratio of aper- 

 ture to focal length, increase the number of stars to such an 

 extent that 10^, or possibly even 10'°, will not be an unreason- 

 able estimate. The following considerations, however, prove 

 that, if there be as many as 10^° stars concerned in the control 

 of the solar motion, their average individual masses must be 

 considerably less than that of the sun (I assume that the ether 

 is devoid of mass, and that matter outside the Galaxy is on the 

 whole symmetrically disposed, and is separated from our stel- 

 lar system by such wide vacant intervals that the galactic 

 motions may be treated independently) : The solar acceleration 

 of gravity at ]N"eptune's orbit being 0*000,651°"' per sec, the 

 galactic acceleration at the distance D = 6000x10'^ km. is : 



f=^rr X 0-000,651 X ( rJ 



M 



= 3-6 X 10-'^ X ^ . 



M 



Assume ^ = 10'°, and / to be uniform for 200,000 years. The 



velocity v = 227 km. per sec. at the end of this time, attained 

 before one-sixth of the distance to the center of attraction has 

 been traversed, is already larger than the maximum velocity 

 permissible. Hence the attractive mass must be less than 

 10'° XM,. 



M 



Let us next try the ratio ^r^ = 10^ with the same radial 



dimensions. I have shown that the motion of the sun can be 

 accounted for, if the central portion of the sphere within the 

 sun's present radius vector contains less than 2,000,000 stars of 

 the same mass as itself. Since the spherical volume of this 

 space is i-oVo" ^^ ^^^^ ^^^^^ volume of the assumed stellar sphere, 

 the supposition of uniform distribution gives 2x10^ stars for 

 the larger volume ; but with central condensation the outer 

 portions of the sphere have not only a more open distribution 

 of stars, but a smaller mass to the unit of volume, and both 

 the number of stars and their mass must be less than 2x10^ 

 li n = 1,000,000,000, and the stars are uniformly distributed, 

 it will take 6,000,000 years for the sun to traverse the distance 



